I need to find the coordinates of x^2 relative to the basis: L= {l0, l1, l2, l3}, and L is the Lagrange basis, but i ain't familiar with this basis. What are the elements of this base?

Surely, if your text asks this question, it has a definition of "Lagrange basis". Anyway, Wikipedia gives {(1/2)(t-1)(t-2), -t(t-2), (1/2)t(t-1)} as a Lagrange basis for quadratic polynomials. They are, basically, the quadratic polynomials that are 0 at x= 0, 1, and 2.